共查询到20条相似文献,搜索用时 15 毫秒
1.
Mathematical Notes - 相似文献
2.
Let
C( \mathbbRm ) C\left( {{\mathbb{R}^m}} \right) be the space of bounded and continuous functions
x:\mathbbRm ? \mathbbR x:{\mathbb{R}^m} \to \mathbb{R} equipped with the norm
|| x ||C = || x ||C( \mathbbRm ): = sup{ | x(t) |:t ? \mathbbRm } \left\| x \right\|C = {\left\| x \right\|_{C\left( {{\mathbb{R}^m}} \right)}}: = \sup \left\{ {\left| {x(t)} \right|:t \in {\mathbb{R}^m}} \right\} 相似文献
3.
V. N. Gabushin 《Mathematical Notes》1968,4(2):624-630
In this article we shall concern ourselves with determining exact (least possible) constants in the inequalities of the form $$\parallel f^{(k)} \parallel _{L_q } \leqslant K\parallel f\parallel _{L_p } ^{\tfrac{{l - k - r - 1 + q - 1}}{{l - r - 1 + p - 1}}} \parallel f^{(l)} \parallel _{L_r } ^{\tfrac{{k - q - 1 + p - 1}}{{l - r - 1 + p^{n - 1} }}} $$ for functions defined on the entire (?∞, ∞), absolutely continuous on any interval together with their (l?1)-th derivatives, and having finite $$l = 2,k = 0,k = 1,q = r = \infty ,1 \leqslant p< \infty $$ is considered. 相似文献
4.
Let = (1,...,d) be a vector with positive components and let D be the corresponding mixed derivative (of order j with respect to the jth variable). In the case where d > 1 and 0 < k < r are arbitrary, we prove that
5.
V. F. Babenko N. V. Parfinovich 《Proceedings of the Steklov Institute of Mathematics》2012,277(1):9-20
Let L ∞,s 1 (? m ) be the space of functions f ∈ L ∞(? m ) such that ?f/?x i ∈ L s (? m) for each i = 1, ...,m . New sharp Kolmogorov type inequalities are obtained for the norms of the Riesz derivatives ∥D α f∥∞ of functions f ∈ L ∞,s 1 (? m ). Stechkin’s problem on approximation of unbounded operators D α by bounded operators on the class of functions f ∈ L ∞,s 1 (? m ) such that ∥?f∥ s ≤ 1 and the problem of optimal recovery of the operator D α on elements from this class given with error δ are solved. 相似文献
6.
7.
New inequalities of Ostrowski type for functions whose derivatives in absolute value are -convex in the second sense are obtained. 相似文献
8.
We establish some Iyengar-type inequalities on time scales for functions whose second derivatives are bounded by using Steffensen’s inequality on time scales. 相似文献
9.
10.
D. S. Skorokhodov 《Ukrainian Mathematical Journal》2012,64(4):575-593
We study the following modification of the Landau?CKolmogorov problem: Let k; r ?? ?, 1 ?? k ?? r ? 1, and p, q, s ?? [1,??]. Also let MM m , m ?? ?; be the class of nonnegative functions defined on the segment [0, 1] whose derivatives of orders 1, 2,??,m are nonnegative almost everywhere on [0, 1]. For every ?? > 0, find the exact value of the quantity $$ \omega_{p,q,s}^{k,r}\left( {\delta; M{M^m}} \right): = \sup \left\{ {{{\left\| {{x^{(k)}}} \right\|}_q}:x \in M{M^m},{{\left\| x \right\|}_p} \leqslant \delta, {{\left\| {{x^{(k)}}} \right\|}_s} \leqslant 1} \right\}. $$ We determine the quantity $ \omega_{p,q,s}^{k,r}\left( {\delta; M{M^m}} \right) $ in the case where s = ?? and m ?? {r, r ? 1, r ? 2}. In addition, we consider certain generalizations of the above-stated modification of the Landau?CKolmogorov problem. 相似文献
11.
Lili Huan Biao Qu Jin-guang Jiang 《Journal of Applied Mathematics and Computing》2010,33(1-2):411-421
In this paper, we present some merit functions for general mixed quasi-variational inequalities, and we obtain the equivalent optimization problems to general mixed quasi-variational inequalities. Since the general mixed quasi-variational inequalities include general variational inequalities, quasi-variational inequalities and nonlinear (implicit) complementarity problems as special cases, our results continue to hold for these problems. In this respect, results obtained in this paper represent an extension of previously known results. 相似文献
12.
13.
14.
For functionsf which have an absolute continuous (n–1)th derivative on the interval [0, 1], it is proved that, in the case ofn>4, the inequality
|
设为首页 | 免责声明 | 关于勤云 | 加入收藏 |
Copyright©北京勤云科技发展有限公司 京ICP备09084417号 |